Pith Number

pith:IWY3SKPG

pith:2014:IWY3SKPGGCSH6YAC4XJ2NRKPVB

not attested not anchored not stored refs pending

Amenability, Critical Exponents of Subgroups and Growth of Closed Geodesics

Rhiannon Dougall, Richard Sharp

arxiv:1411.6817 v3 · 2014-11-25 · math.DS · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IWY3SKPGGCSH6YAC4XJ2NRKPVB}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T01:36:34.176964Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

45b1b929e630a47f6002e5d3a6c54fa84cdee47f8085a880466aeac643da6a2b

Aliases

arxiv: 1411.6817 · arxiv_version: 1411.6817v3 · doi: 10.48550/arxiv.1411.6817 · pith_short_12: IWY3SKPGGCSH · pith_short_16: IWY3SKPGGCSH6YAC · pith_short_8: IWY3SKPG

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/IWY3SKPGGCSH6YAC4XJ2NRKPVB \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 45b1b929e630a47f6002e5d3a6c54fa84cdee47f8085a880466aeac643da6a2b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3baad457d085464940ea4f1c945ecb23d1c956b68d44dbc0c8cbfa412a91476b",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2014-11-25T11:13:55Z",
    "title_canon_sha256": "1c0b445647251694c45d8c255475c2a6ff6476d0d81043bf738eaac70830a3c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.6817",
    "kind": "arxiv",
    "version": 3
  }
}